Scanning lens and optical scanner using the same

Abstract: An optical scanner including a semiconductor laser device, aperture, collimator, cylindrical lens, polygonal mirror and one fϑ lens element molded from plastics. The first surface of the fϑ lens in a deflecting plane (or the plane formed by the principal rays of light as deflected by the polygonal mirror) is aspheric whereas the second lens surface is toric. When taken in the deflecting plane, the first lens surface has a positive value of the near-axis radius of curvature and, hence, it is convex toward the polygonal mirror. Taken in a plane crossing the deflecting plane at right angles, the first lens surface forms an arc of a circle having a negative value of the radius of curvature and, hence, it is concave toward the polygonal mirror. When taken in the deflecting plane, the second lens surface forms an arc of a circle having a negative value of the radius of curvature and, hence, it is convex toward the scanning surface.

Description: BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a scanning lens and an optical scanner that uses it. More particularly, the invention relates to a single-element scanning lens for use as an f lens in laser scanning optics, as well as an optical scanner equipped with this scanning lens. 2. Description of the Related Art Optical scanners are extensively used with optical printers, digital copiers and the like. Such optical scanners employ a deflector such as a polygonal mirror for deflecting incident light at a constant angular velocity in a direction corresponding to the main scanning direction, and an f lens as a scanning lens. The f lens has two functions; according to one function, a laser beam that issues typically from a semiconductor laser device and which has been deflected by the deflector is focused as a spot on a scanning surface such as a photoreceptor drum or belt and the other function is to move the beam spot over the scanning surface at a constant speed. In most cases, the f lens is provided with the capability by which the position of a deflecting point on the deflector and the position of a beam spot on the scanning surface are rendered to satisfy a conjugated relationship in a plane crossing at right angles with the plane formed by the deflected laser beam. A cylindrical lens is positioned on the side of the deflector where the laser beam is launched and it has a lens powder in a direction corresponding to the sub-scanning direction. The f lens combines with this cylindrical lens to constitute tilt-correcting optics which corrects optically any inclination of reflecting surfaces of the deflector and which is capable of producing a substantially circular beam spot. Many of the commercial f lenses available today are optics that are composed of two or more lens elements but they suffer from the disadvantage of complexity in construction. To solve this problem, f lenses composed of only one lens element have been proposed as simple optics. Japanese Patent Unexamined Publication Nos. Sho. 57-144518, Sho. 63-50812 and Hei. 3-55513 teach one-element f lenses having a toric surface on one side and a spherical, cylindrical or toric surface on the other side. Japanese Patent Unexamined Publication Nos. Sho. 62-138823, Hei. 4-50908 and Hei. 5-45580 teach f lenses having an aspheric surface. However, the conventional f lenses have their own problems. The f lens described in Japanese Patent Unexamined Publication No. Sho. 57-144518 which is solely composed of toric surfaces provides no better performance than a single spherical lens element when compared on the main scanning surface and, hence, it suffers from the disadvantage of small latitude in design, limited extent to which imaging performance can be insured in terms of f characteristics and curvature of field, and the resulting failure to achieve high image resolution. If one strains to assure satisfactory imaging performance, the center thickness of the lens has to be increased as described in Japanese Patent Unexamined Publication Nos. Sho. 63-50812 and Hei. 3-55513 but this only results in increased difficulty in lens manufacture. With a view to eliminating these drawbacks, Japanese Patent Unexamined Publication Nos. Sho. 62-138823 and Hei. 4-50908 have proposed f lenses that adopt an aspheric surface in order to provide improved imaging performance. However, these f lenses are so complex in shape as to have no rotating axis and, hence, they are very difficult to design and manufacture. The f lens described in Japanese Patent Unexamined Publication No. Hei. 5-45580 is such that a cross-sectional shape taken in the main scanning direction is of a meniscus convex to the scanning surface and it adopts an aspheric surface having a rotating axis. However, light condensing optics must be provided on the side of a tenon-shaped mirror (deflector) where incident light is launched. In addition, the f characteristics of the lens are substantially associated with constant speed and electrical correction must be made to achieve linearity but, then, the overall equipment becomes complicated and costly. SUMMARY OF THE INVENTION The present invention has been accomplished under these circumstances and has an object to provide a one-element scanning lens that adopts a simple enough shape to assure not only high performance but also ease in design and manufacture. Another object of the invention is to provide an optical scanner using such scanning lens. To achieve the first object, the invention provides a scanning lens in accordance with claim 1. To achieve the second object, the invention provides an optical scanner according to claim 3. BRIEF DESCRIPTION OF THE DRAWINGS The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and, together with the description, serve to explain the objects, advantages and principles of the invention. In the drawings, Fig. 1(a) is a simplified cross-sectional view showing the shape of an f lens of Embodiment 1 as it is cut across the deflecting plane; Fig. 1(b) is a simplified cross-sectional view of the shape of the f lens as it is cut across a plane crossing the deflecting plane at right angles; Fig. 2 is an illustration of the shape of the surface of the f lens of Embodiment 1 which is directed toward a polygonal mirror; Fig. 3 is an illustration of the shape of the surface of the f lens of Embodiment 1 which is directed toward a photoreceptor drum; Fig. 4 is a perspective view of an optical scanner using the f lens of Embodiment 1; Fig. 5 is an illustration of the shapes of the f lenses in Embodiments 1 to 24, respectively, as they are cut across the deflecting plane; Fig. 6(a) is a graph showing the curvatures of field that develop in Embodiment 1; Fig. 6(b) is a graph showing the f characteristics of Embodiment 1; Fig. 7(a) is a graph showing the curvatures of field that develop in Embodiment 2; Fig. 7(b) is a graph showing the f characteristics of Embodiment 2; Fig. 8(a) is a graph showing the curvatures of field that develop in Embodiment 3; Fig. 8(b) is a graph showing the f characteristics of Embodiment 3; Fig. 9(a) is a graph showing the curvatures of field that develop in Embodiment 4; Fig. 9(b) is a graph showing the f characteristics of Embodiment 4; Fig. 10(a) is a graph showing the curvatures of field that develop in Embodiment 5; Fig. 10(b) is a graph showing the f characteristics of Embodiment 5; Fig. 11(a) is a graph showing the curvatures of field that develop in Embodiment 6; Fig. 11(b) is a graph showing the f characteristics of Embodiment 6; Fig. 12(a) is a graph showing the curvatures of field that develop in Embodiment 7; Fig. 12(b) is a graph showing the f characteristics of Embodiment 7; Fig. 13(a) is a graph showing the curvatures of field that develop in Embodiment 8; Fig. 13(b) is a graph showing the f characteristics of Embodiment 8; Fig. 14(a) is a graph showing the curvatures of field that develop in Embodiment 9; Fig. 14(b) is a graph showing the f characteristics of Embodiment 9; Fig. 15(a) is a graph showing the curvatures of field that develop in Embodiment 10; Fig. 15(b) is a graph showing the f characteristics of Embodiment 10; Fig. 16(a) is a graph showing the curvatures of field that develop in Embodiment 11; Fig. 16(b) is a graph showing the f characteristics of Embodiment 11; Fig. 17(a) is a graph showing the curvatures of field that develop in Embodiment 12; Fig. 17(b) is a graph showing the f characteristics of Embodiment 12; Fig. 18(a) is a graph showing the curvatures of field that develop in Embodiment 13; Fig. 18(b) is a graph showing the f characteristics of Embodiment 13; Fig. 19(a) is a graph showing the curvatures of field that develop in Embodiment 14; Fig. 19(b) is a graph showing the f characteristics of Embodiment 14; Fig. 20(a) is a graph showing the curvatures of field that develop in Embodiment 15; Fig. 20(b) is a graph showing the f characteristics of Embodiment 15; Fig. 21(a) is a graph showing the curvatures of field that develop in Embodiment 16; Fig. 21(b) is a graph showing the f characteristics of Embodiment 16; Fig. 22(a) is a graph showing the curvatures of field that develop in Embodiment 17; Fig. 22(b) is a graph showing the f characteristics of Embodiment 17; Fig. 23(a) is a graph showing the curvatures of field that develop in Embodiment 18; Fig. 23(b) is a graph showing the f characteristics of Embodiment 18; Fig. 24(a) is a graph showing the curvatures of field that develop in Embodiment 19; Fig. 24(b) is a graph showing the f characteristics of Embodiment 19; Fig. 25(a) is a graph showing the curvatures of field that develop in Embodiment 20; Fig. 25(b) is a graph showing the f characteristics of Embodiment 20; Fig. 26(a) is a graph showing the curvatures of field that develop in Embodiment 21; Fig. 26(b) is a graph showing the f characteristics of Embodiment 21; Fig. 27(a) is a graph showing the curvatures of field that develop in Embodiment 22; Fig. 27(b) is a graph showing the f characteristics of Embodiment 22; Fig. 28(a) is a graph showing the curvatures of field that develop in Embodiment 23; Fig. 28(b) is a graph showing the f characteristics of Embodiment 23; Fig. 29(a) is a graph showing the curvatures of field that develop in Embodiment 24; and Fig. 29(b) is a graph showing the f characteristics of Embodiment 24. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, embodiments of the invention will be described in detail with reference to the accompanying drawings. As shown schematically in Fig. 4, an optical scanner of Embodiment 1 of the invention has a semiconductor laser device 10 as a light source and an aperture 12 and a collimator 14 for shaping the light beam from the semiconductor laser device 10 to parallel rays are arranged in that order on the side of the laser 10 from which laser beam issues. A cylindrical lens 16 is positioned on the side of the collimator 14 from which the collimated laser beam emerges. The cylindrical lens 16 has a lens power in a direction corresponding to the sub-scanning direction and permits the collimated laser beam to form a line image elongated in a direction corresponding to the main scanning direction (indicated by an arrow). A polygonal mirror 18 which reflects the incident laser beam and deflects it at a constant angular velocity in a direction corresponding to the main scanning direction is positioned in such a way that a reflecting surface 20 will coincide either with the position where the line image forms or with a nearby area. An f lens 22 which is a single scanning lens element formed of plastic amorphous polyolefin is provided on the side of the polygonal mirror 18 from which the reflected laser beam emerges. The f lens 22 converges the reflected laser beam in such a way that a substantially circular beam spot is scanned at a constant speed over the surface of a photoreceptor drum 26 which serves as a scanning surface. For an installation-related reason, a reflector mirror 24 with which the laser beam issuing from the f lens 22 is reflected towards the photoreceptor drum 26 is provided between the two components. In the embodiment under consideration, the cylindrical lens 16 is positioned on the entrance side of the polygonal mirror 18 to constitute pre-polygonal optics and this mirror focuses the light beam from the semiconductor laser device 10 in such a way that a line image elongated in a direction corresponding to the main scanning direction is formed on the reflecting surface 20. The laser beam is then deflected by the polygonal mirror 18 at a constant angular velocity in a direction corresponding to the main scanning direction and subsequently launched into the f lens 22, which performs scanning over the photoreceptor drum 26 in the main scanning direction at a constant speed. The f lens 22 also performs anti-tilt correction to correct any uneven pitches in the sub-scanning direction. The cylindrical lens 16 also works to form a substantially circular beam spot on the photoreceptor drum 26. Fig. 1(a) shows the shapes of individual lenses in the deflecting plane of the f lens 22 (or the plane which the principal rays of laser beam deflected by polygonal mirror 18 will form) and Fig. 1(b) shows the lens shapes in a plane crossing the deflecting plane at right angles (or the plane that includes the optical axis of the f lens 22 and which crosses the deflecting plane at right angles). The lens surface S1 of the f lens 22 which is directed towards the polygonal mirror 18 (or deflecting means) is aspheric whereas the surface S2 directed towards the photoreceptor drum 26 (or scanning surface) is toric. As shown in Fig. 2, the aspheric lens surface S1 is produced by rotating the curve L1 expressed by the following equation (1) about the axis R1 which is a straight line in the deflecting plane and parallel to the y-axis of an assumed xy plane in the deflecting plane that has as the origin the point O of intersection between the optical axis A and the lens surface S1 and which has the x-axis extending along the optical axis A: x = y 2 /{ R1M + R1M 2 -(1+ K ) y 2 } + Ay 4 + By 6 + Cy 8 + Dy 10 where R1M is a near-axis radius of curvature of the aspheric lens surface, K is a conic constant, and A, B, C and D are aspheric coefficients of higher orders. Hence, when taken in the deflecting plane, the lens surface S1 is convex toward the polygonal mirror 18 since R1M, or its near-axis radius of curvature is positive (the sign of radius of curvature is assumed to be positive for the distance measured in the direction in which the incident laser beam is launched or approaches, and negative for the distance measured in the direction in which the incident laser beam travels); on the other hand, when taken in the plane crossing the deflecting plane at right angles, the lens surface S1 is concave toward the polygonal mirror 18 or convex toward the photoreceptor drum since it forms an arc of a circle with R1S, or its radius of curvature in the plane crossing the deflecting plane at right angles, being negative. The radius of curvature R1S corresponds to the distance between the rotating axis R1 and the lens surface S1 in the axial direction. As shown in Fig. 3, the toric lens surface S2 is produced by rotating the arc L2 of a circle, having the radius of curvature R2S and located in the plane crossing the deflecting plane at right angles, about the axis R2 that is a straight line in the plane crossing the deflecting plane at right angles, that crosses the optical axis A at right angles and which is apart from the arc L2 of a circle by the distance R2M. Therefore, the lens surface S2 is such a toric surface that the arcs of circles in the deflecting plane and in the plane crossing that deflecting plane at right angles are convex toward the photoreceptor drum. The radius of curvature R2M of the arc of a circle in the deflecting plane corresponds to the distance between the rotating axis R2 and the lens surface S2 in the axial direction. To attain balance between f and imaging characteristics using only one f lens element in the embodiment under consideration, the absolute value of R1M, or the near-axis radius of curvature of the aspheric surface, is preferably adjusted to be greater than the absolute value of R2M, or the radius of curvature of the arc of a circle formed by the toric surface in the deflecting plane. Further, in order to insure that the conjugated relationship between a point of deflection and the scanning surface is assured without undue strain, the absolute value of R1S, or the radius of curvature of the arc of a circle formed by the aspheric surface in the plane crossing the deflecting plane at right angles is preferably adjusted to be greater than the absolute value of R2S, or the radius of curvature of the arc of a circle formed by the toric surface in the plane crossing the deflecting plane at right angles. Thus, the f lens is preferably designed to satisfy the following conditions: R1M/R2M<-1 R1S/R2S>1 Table 1 shows the dimensions of various parts of the f lens 22 fabricated in the embodiment (Embodiment 1) using amorphous polyolefin, as well as the values of R2M/f and R2S/f. In Table 1, n signifies the refractive index of the amorphous polyolefin; d1, the axial distance between lens surfaces S1 and S2; d0, the axial distance from the reflecting surface 20 of the polygonal mirror 18 to the lens surface S1 of the f lens which is directed toward the polygonal mirror 18; d2, the axial distance between the lens surface S2 of the f lens which is directed toward the photoreceptor drum 26 and the surface of the drum (for d0, d1 and d2, see Fig. 1(a)); f, the focal length of the f lens in the deflecting plane; , the maximum viewing angle; and λ, the wavelength of laser beam. The dimensions of the various parts of the f lens are expressed in millimeters. The distance from the center of rotation of the polygonal mirror 18 to the reflecting surface 20 is 17 mm, and the incident light on the polygonal mirror is assumed to be launched in the axial direction. This assumption is made for the simplicity in the description of the embodiment and the results will be substantially the same if other angles of incidence are considered. The curvatures of field that develop in the f lens specified in Table 1 are shown in Fig. 6(a), and the f characteristics of the same lens are shown in Fig. 6(b) as expressed by the departure from the ideal position. The dashed line in Fig. 6(a) refers to the curvature of field that occurs in the main scanning direction and the solid line in the sub-scanning direction. Tables 2 to 24 show the dimensions of various parts of the f lenses fabricated in Embodiments 2 to 24, respectively, for use in an optical scanner of the same type as shown in Fig. 4, as well as the values of R2M/f and R2S/f. The curvatures of field that develop in the f lenses of Embodiments 2 to 24 are shown in Figs. 7(a) to 29(a), respectively, and the f characteristics of those lenses are shown in Figs. 7(b) to 29(b), respectively. The axes of each graph are graduated on the same scale as in Fig. 6(a) or 6(b). In Embodiments 2 to 12, plastic amorphous polyolefin was used as an optical material (this is the same as in Embodiment 1) but the value of d0 or d1 was varied as a parameter. The ideal focal length which was the reference for the f characteristics was 143.2394488 mm. In Embodiments 13 to 16, plastic polycarbonate (n = 1.572) was used as an optical material and the value of d0 or d1 was varied as a parameter. The ideal focal length which was the reference for the f characteristics was 143.2394488 mm. In Embodiments 17 to 24, plastic amorphous polyolefin was used as an optical material and the value of d0 or d1 was varied as a parameter. The ideal focal length which was the reference for the f characteristics was 171.8873385 mm. Cross sections of the f lenses of Embodiments 1 to 24 as taken through the deflecting plane are shown in (1) to (24) of Fig. 5, respectively. As one can see from Figs. 7(a) to 29(b), the curvatures of field were corrected satisfactorily and the departure from the ideal position was within approximately 0.2 mm in all cases, indicating that the f characteristics of all lenses were satisfactory. Embodiments 1 to 24 refer to the case of molding the f lens of plastic but it should be noted that equally good results can be attained even if the lens is manufactured from glass. As described on the foregoing pages, the one-element scanning lens according to the first aspect of the invention adopts a simple enough shape to assure not only high performance but also ease in design and manufacture. On account of using this one-element scanning lens which adopts a simple enough shape to assure not only high performance but also ease in design and manufacture, the optical scanner according to the second aspect of the invention can be manufactured in a smaller size and at a lower cost.

Claims: A scanning lens which is a single lens element (22) for being positioned between deflecting means (18) for deflecting an incident light beam in a predetermined direction at a constant angular velocity and a scanning surface (26) for converging the incident light beam in such a way that a beam spot is scanned at a constant speed over said scanning surface (26), said scanning lens comprising a first and a second lens surface, characterized in that said first lens surface (51) has a rotating axis R 1 that is located in a deflecting plane formed by principal rays of light beam deflected by said deflecting means (18) and which crosses an optical axis (A) of said scanning lens at right angles, wherein a curve (L1) said first lens surface forms by crossing the deflecting plane is convex toward said deflecting means (18) in the neighborhood of the optical axis (A) and wherein an arc of a circle said first lens surface forms by crossing a plane crossing said deflecting plane at right angles is formed of an aspheric surface convex toward the scanning surface (26); and said second lens surface (S2) has a rotating axis (R 2 ) that is located in the plane crossing the deflecting plane at right angles and which crosses the optical axis (A) at right angles, wherein arcs of circles said second lens surface forms by crossing the deflecting plane and the plane crossing the deflecting plane at right angles are formed of toric surfaces convex toward the scanning surface (26), wherein said first and second lens surfaces, S 1 and S 2 , satisfy the following conditions: R1M/R2M<-1 R1S/R2S>1 -0.9<R2M/f<-0.55 -0.16<R2S/f<-0.08 where R1M is a near-axis radius of curvature of the aspheric lens surface, R1S is a radius of curvature of an arc of a circle of the aspheric lens surface in the plane crossing the deflecting plane at right angles, R2M is a radius of curvature of an arc of a circle of the toric lens surface in the deflecting plane, R2S is a radius of curvature of an arc of a circle of the toric lens surface in the plane crossing the deflecting plane at right angles, and f is a focal length of said scanning lens in the deflecting plane, provided that the sign of radius of curvature is positive when the curvature is convex in a direction in which the incident light beam is launched and negative when it is convex in a direction in which the incident light beam travels. The scanning lens according to claim 1, characterized in that the aspheric lens surface (S1) is produced by rotating a curve (L1) expressed by the following equation about an axis (R1) which is a straight line parallel to a y-axis of an assumed xy plane in the deflecting plane that has as the origin a point (O) of intersection between the optical axis (A) and the first lens surface (S1) and which has an x-axis extending along the optical axis (A). x = y 2 /{ R1M + R1M 2 -(1+ K ) y 2 }+ Ay 4 + By 6 + Cy 8 + Dy 10 where K is a conic constant, and A, B, C and D are aspheric coefficients of higher orders. An optical scanner comprising: collimating means (14) for converting a light beam from a light source (10) to substantially parallel rays; imaging means (16) for permitting the parallel rays to form a line image elongated in a direction corresponding to a main scanning direction; deflecting means (18) that has a reflecting surface (20) either in a position where the line image forms or in the neighborhood of said position and which deflects the incident light beam at a constant angular velocity in the direction corresponding to the main scanning direction; and characterized in that it further comprises a single scanning lens element (22) according to claim 1. The optical scanner according to claim 3, characterized in that it comprises a single scanning lens element according to claim 2.

Inventors: OTA AKIRA, OTA, AKIRA, OTA, AKIRA, IWATSUKI WORKS
Applicants: FUJI XEROX CO LTD, FUJI XEROX CO., LTD.
Application year: 1994
Main classification: G02B13
IPC codes: G02B13, G02B26